Differential Calculus

Let $f: [0,\infty )\to [0,\infty )$ be given by $f\left(x\right)=\sum _{i=1}^{10}\left(\frac{x^i}{i}\right)$. If $f^{\text{'}}\left(x\right)$ denotes the derivative of $f\left(x\right),$ then the value of $\underset{x\to 1}{\lim }\frac{f^{\text{'}}\left(x\right)-10}{x-1}$ is

Let $f,g$ and $h$ be the real valued functions defined on $\mathrm{ℝ}$ as $f\left(x\right)=\begin{array}{cc}\frac{x}{\left.x\right|},& x\ne 0\\ 1,& x=0\end{array}, g\left(x\right)=\begin{array}{cc}\frac{\sin \left(x+1\right)}{\left(x+1\right)},& x\ne -1\\ 1,& x=-1\end{array}$and $h\left(x\right)=2\left.x\right]-f\left(x\right)$, where $\left.x\right]$ is the greatest integer $\le x$. Then the value of $\underset{x\to 1}{\lim }g\left(h\left(x-1\right)\right)$ is